数学物理方法课件
1 1 u ( x, t ) = [Φ ( x + at ) + Φ ( x at )] + ∫ Ψ (ξ )dξ 2 2a x atx + at 1 1 [ ( x + at ) + ( x at )] + ∫ ψ (ξ )dξ 2 2a x at u ( x, t ) x + at 1 1 [ ( x + at ) ( x at )] + ∫ xψ (ξ )dξ 2 2a at
x + at
(t ≤ x / a ) (t ≥ x / a)
(t ≥ x / a )
1 2a
x + at
x at
∫
Ψ (ξ ) dξ =x + at
1 2a
x + at
∫0
Ψ (ξ ) dξ +0
1 2a
x at
∫
0
Ψ (ξ ) dξ = 1 2ax + at
1 2a
x + at
∫0
ψ (ξ ) dξ +10
1 2a
x at
∫ ψ ( ξ ) dξ
0
=
1 2a
∫ ψ (ξ ) dξ + 2 a ∫0
1
ψ ( ξ ) d ( ξ ) =
( x at )
∫ ψ (ξ ) dξ + 2 a ∫ ψ (ξ ) d (ξ )0 at x